I had the same or similar error. If I attempted an install of just this service with logging I them got error 1920 from the msiexec log files.
Turns out (in my case) it caused by the wrong version of msvcr100.dll in the windows\system32 folder. This was on a 64 bit version of windows7. The version in this folder is supposed to be a x64 version of the dll, but was a x86 version instead. I used the sysinternals process monitor to find out the cause (for my situation). - See https://social.msdn.microsoft.com/Forums/vstudio/en-US/a0a2608a-3102-40f8-93ce-2 53d08d91406/32bit-version-of-msvcr100dll-is-installed-in-64bit-cwindowssystem32- directory?forum=vcgeneral
The solution is to first rename this dll e.g. to msvcr100.x86.dll and to then to download and re-install the
using this link http://www.microsoft.com/en-us/download/details.aspx?id=13523
You may also want to install the 32bit/x86 version of this package too.
http://www.microsoft.com/en-us/download/details.aspx?id=8328
Once you have done this the service will start and you can re-install/repair iTunes.